## anonymous 5 years ago power series solution y' + y/x = 0

1. myininaya

xy'+y=0 (xy)'=0 xy=C y=C/x

2. anonymous

$dy/dx + y/x = 0$ $dy/dx = -y/x$ $dy/y = -dx/x$ $\int\limits(dy/y) = \int\limits(-dx/x)$ $lny = -lnx + lnk$ $lny = -\ln(x/k)$ $e ^{lny} = e^{-\ln(x/k)}$ $y = k/x$, where k is an arbitrary constant.